Abstract
There are certain optimal control problems with state constraints for which the standard versions of the necessary conditions of optimality are unable to provide information to select minimizers. In the recent years, there has been some literature on stronger forms of the maximum principle, the so-called nondegenerate necessary conditions, that are informative for those problems. These conditions can be applied when certain constraint qualifications are satisfied. However, when the state constraints have higher index (i.e. their first derivative with respect to time does not depend on the control) the nondegenerate necessary conditions existent in the literature cannot be applied. This is because their constraint qualifications are never satisfied for higher index state constraints. Here, we provide a nondegenerate form of the necessary conditions that can be applied to problems with higher index state constraints. We note that control problems with higher index state constraints arise frequently in mechanical systems, when there is a constraint on the position (an obstacle in the path, for example) and the control acts as a force or acceleration.

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Abstract
This paper presents new results improving by a factor of 10 the accuracy of an Odd-DFT based frequency estimation algorithm. These results are shown to be robust to the influence of additive noise and compare favorably to other non-iterative frequency domain estimation algorithms. A perspective is given oil possible application areas, namely those involving real-time constraints.

Abstract
This paper presents and analyses a new method for the detection of the point of collapse and a new index for the definition of the distance of the voltage collapse point. This paper demonstrates that a point of a Newton-Raphson power flow becomes singular when the full sum of the partial derivate of the reactive power equations in relation to the voltage level is approximately constant. Numerical experiments using standard IEEE 14 and 57 bus systems show that the proposed method can compute the voltage collapse point using several different scenery of load increase, line or generator outages. The methodology proposed may be easily implemented in any power flow program.

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Abstract